Final answer:
To determine the mass of hydrogen produced by Sample B of CH4 when it decomposes, we utilize the constant ratio of carbon to hydrogen in methane. By maintaining the 3:1 ratio in 23.0 grams of carbon, we find that 7.67 grams of hydrogen are produced, which does not match any of the provided options.
Step-by-step explanation:
When Sample A of methane (CH4) decomposes, it produces 35.0 grams of carbon (C) and 2.04 grams of hydrogen (H). The ratio of the mass of carbon to the mass of hydrogen in methane is derived from the molar mass and stoichiometry of methane. The molar mass of carbon is 12.01 g/mol and hydrogen is 1.008 g/mol, thus the molar mass of methane is approximately 16.04 g/mol, which reflects a ratio of C:H as 12.01 g/mol:C to 4.032 g/mol:H (4 hydrogen atoms). Therefore, the mass ratio of carbon to hydrogen in methane is 12.01:(4 x 1.008) = 3:1.
Given that Sample A has a mass of 35.0 grams of C to 2.04 grams of H, Sample B produces 23.0 grams of C. To maintain the 3:1 ratio, we divide 23.0 grams of C by 3 to find the mass of hydrogen produced by Sample B:
23.0 g C ÷ 3 = 7.67 g C (1 gram of H for every 3 grams of C)
Therefore, Sample B produces 7.67 grams of hydrogen. Amongst the given options, none match this calculation, possibly indicating a mistake in the options or the need for additional information.